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RUN REVIEW · Mathematical Methods · Units 3 & 4 · Tech-free

Anonymous Student · guest

12 Oct 2026, 11:37 p.m.

13Serious score
01 During a one-minute revision round: The graph of \(y=f(x-2)+3\) is translated
A 2 right and 3 down This does not satisfy the stated relationship.
B 2 right and 3 up Horizontal translation uses the opposite sign inside.
C 3 right and 2 down This does not satisfy the stated relationship.
D 2 left and 3 up This does not satisfy the stated relationship.

Written for icaijy.com · U1–2 · Transformations · answered at 8728 ms

02 A student is checking a worked solution. \(P(A\mid B)=\)
A \(\frac{P(A)}{P(B)}\) This does not satisfy the stated relationship.
B \(P(A\cup B)\) This does not satisfy the stated relationship.
C \(\frac{P(A\cap B)}{P(B)}\) Restrict the sample space to B.
D \(P(A)P(B)\) always This does not satisfy the stated relationship.

Written for icaijy.com · U3–4 · Conditional probability · answered at 12383 ms

03 A student is checking a worked solution. The period of \(\sin(2x)\) is
A \(4\pi\) This does not satisfy the stated relationship.
B \(2\pi\) This does not satisfy the stated relationship.
C \(\pi\) Period is 2π/2 = π.
D \(\pi/2\) This does not satisfy the stated relationship.

Written for icaijy.com · U1–2 · Trigonometry · answered at 14424 ms

04 Which response best completes this VCE-style item? The graph of \(y=f(x-2)+3\) is translated
A 3 right and 2 down This does not satisfy the stated relationship.
B 2 right and 3 down This does not satisfy the stated relationship.
C 2 right and 3 up Horizontal translation uses the opposite sign inside.
D 2 left and 3 up This does not satisfy the stated relationship.

Written for icaijy.com · U1–2 · Transformations · answered at 19780 ms

05 A student is checking a worked solution. The vertex of \(y=(x-2)^2-5\) is
A \((2,-5)\) Vertex form y=(x−h)²+k has vertex (h,k).
B \((-5,2)\) This does not satisfy the stated relationship.
C \((-2,-5)\) This does not satisfy the stated relationship.
D \((2,5)\) This does not satisfy the stated relationship.

Written for icaijy.com · U1–2 · Quadratics · answered at 23161 ms

06 The solution of \(|x|<3\) is
A \((-3,3)\) Distance from zero must be less than three.
B \([-3,3]\) This does not satisfy the stated relationship.
C \(x>3\) This does not satisfy the stated relationship.
D \(({-\infty},-3)\cup(3,\infty)\) This does not satisfy the stated relationship.

Written for icaijy.com · U1–2 · Algebra · answered at 26452 ms

07 During a one-minute revision round: For \(a>1\), \(y=a^x\) is
A undefined at x=0 This does not satisfy the stated relationship.
B periodic This does not satisfy the stated relationship.
C strictly increasing An exponential with base greater than one increases.
D strictly decreasing This does not satisfy the stated relationship.

Written for icaijy.com · U1–2 · Exponentials · answered at 32423 ms

08 A student is checking a worked solution. The graph of \(y=f(x-2)+3\) is translated
A 2 right and 3 down This does not satisfy the stated relationship.
B 3 right and 2 down This does not satisfy the stated relationship.
C 2 left and 3 up This does not satisfy the stated relationship.
D 2 right and 3 up Horizontal translation uses the opposite sign inside.

Written for icaijy.com · U1–2 · Transformations · answered at 37088 ms

09 A student is checking a worked solution. If \(f(x)=x^3\), then \(f\prime(x)=\)
A \(x^4/4\) This does not satisfy the stated relationship.
B \(x^2\) This does not satisfy the stated relationship.
C \(3x^2\) Apply the power rule.
D \(3x\) This does not satisfy the stated relationship.

Written for icaijy.com · U1–2 · Differentiation · answered at 39889 ms

10 During a one-minute revision round: If \(P(3)=0\), then a factor of \(P(x)\) is
A \(x^3\) This does not satisfy the stated relationship.
B \(x-3\) The factor theorem gives x−3.
C \(x+3\) This does not satisfy the stated relationship.
D \(3x-1\) This does not satisfy the stated relationship.

Written for icaijy.com · U1–2 · Polynomials · answered at 42305 ms

11 Which response best completes this VCE-style item? For events A and B, \(P(A\cup B)=\)
A \(P(A)P(B)\) This does not satisfy the stated relationship.
B \(1-P(A)\) This does not satisfy the stated relationship.
C \(P(A)+P(B)-P(A\cap B)\) Subtract the intersection counted twice.
D \(P(A)+P(B)\) This does not satisfy the stated relationship.

Written for icaijy.com · U1–2 · Probability · answered at 46738 ms

12 A student is checking a worked solution. Increasing sample size while all else is fixed makes a confidence interval generally
A wider This does not satisfy the stated relationship.
B narrower Standard error decreases as sample size grows.
C unchanged This does not satisfy the stated relationship.
D centred at zero This does not satisfy the stated relationship.

Written for icaijy.com · U3–4 · Confidence intervals · answered at 49984 ms

13 Which response best completes this VCE-style item? \(\log_a(xy)\) equals
A \(\log_a(x+y)\) This does not satisfy the stated relationship.
B \(\log_a x\log_a y\) This does not satisfy the stated relationship.
C \(x+y\) This does not satisfy the stated relationship.
D \(\log_a x+\log_a y\) The logarithm of a product is a sum.

Written for icaijy.com · U1–2 · Logarithms · answered at 56199 ms

14 During a one-minute revision round: \(\frac d{dx}[xe^x]=\)
A \(e^x\) This does not satisfy the stated relationship.
B \(x^2e^x\) This does not satisfy the stated relationship.
C \(e^x(1+x)\) Use uv′+u′v.
D \(xe^x\) This does not satisfy the stated relationship.

Written for icaijy.com · U3–4 · Product rule · not answered before time expired

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